Equations for Simulations in SigmaPlot or similar:

Product Concentration:

-((k*T/h)*exp(-C/(R*T))*E/(((k*T/h)*exp(-I/(R*T))*exp((-Q/R)*(1/T-1/S)))))*exp(-((k*T/h)*exp(-I/(R*T))*exp((-Q/R)*(1/T-1/S))/(1+exp((-Q/R)*(1/T-1/S))))*D)+(k*T/h)*exp(-C/(R*T))*E/((k*T/h)*exp(-I/(R*T))*exp((-Q/R)*(1/T-1/S)))

Initial Rates:

(k*T/h)*exp(-C/(R*T))*E/(1+exp((-Q/R)*(1/T-1/S)))

Progress Curves (Rates):

((k*T*exp(-C/(R*T))*E)*exp(-(k*T*exp(-I/(R*T))*exp((Q*(1/S-1/T))/R)*t)/(h*(1+exp(Q*(1/S-1/T)/R)))))/(h*(1+exp(Q*(1/S-1/T)/R)))

Classical Model (Rates):

(((k*T)/h)*exp(-(C/(R*T))))*(E)*exp(-(((k*T)/h)*exp(-(I/(R*T)))*t))

Constants:

k = 1.38E-23
h = 6.63E-34
R = 8.32

Parameters:

E = E0
I = EAi
C = EAcat
Q = Heq
S = Teq

Variables:

T = Temperature
D = time


Equations for Simulations and calculation of Residuals in Excel:

Excel Product Concentration Simulation:

=(-((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$6/(8.32*Data!B$1))*'Settings-Output'!$C$4/(((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$5/(8.32*Data!B$1))*exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8)))))*exp(-((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$5/(8.32*Data!B$1))*exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8))/(1+exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8))))*Data!$A2)+(1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$6/(8.32*Data!B$1))*'Settings-Output'!$C$4/((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$5/(8.32*Data!B$1))*exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8))))

Excel Product Concentration Residual Calculation (= Experimental - Simulation):

=Data!B2-(-((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$6/(8.32*Data!B$1))*'Settings-Output'!$C$4/(((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$5/(8.32*Data!B$1))*exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8)))))*exp(-((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$5/(8.32*Data!B$1))*exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8))/(1+exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8))))*Data!$A2)+(1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$6/(8.32*Data!B$1))*'Settings-Output'!$C$4/((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$5/(8.32*Data!B$1))*exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8))))

Excel Product Concentration Residual Percentage Calculation (= Experimental - Simulation):

=((Data!B2-(-((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$6/(8.32*Data!B$1))*'Settings-Output'!$C$4/(((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$5/(8.32*Data!B$1))*exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8)))))*exp(-((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$5/(8.32*Data!B$1))*exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8))/(1+exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8))))*Data!$A2)+(1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$6/(8.32*Data!B$1))*'Settings-Output'!$C$4/((1.38E-23*Data!B$1/6.63E-34)*exp(-'Settings-Output'!$E$5/(8.32*Data!B$1))*exp((-'Settings-Output'!$E$7/8.32)*(1/Data!B$1-1/'Settings-Output'!$E$8)))))/Data!B2)*100

